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  • Bulk-boundary correspondence for vacuum asymptotically Anti-de Sitter spacetimes

    Abstract: The AdS/CFT conjecture in physics posits the existence of a correspondence between gravitational theories in asymptotically Anti-de Sitter (aAdS) spacetimes and field theories on their conformal boundary. In this presentation, we prove rigorous mathematical statements toward this conjecture. In particular, we show there is a one-to-one correspondence between aAdS solutions of the Einstein-vacuum equations and a suitable space of data on […]

  • CMSA-Combinatorics-Physics-and-Probability-Seminar-3.15.2022-1

    Flip processes

    Abstract: We introduce a class of random graph processes, which we call \emph{flip processes}. Each such process is given by a \emph{rule} which is just a function $\mathcal{R}:\mathcal{H}_k\rightarrow \mathcal{H}_k$ from all labelled $k$-vertex graphs into itself ($k$ is fixed). The process starts with a given $n$-vertex graph $G_0$. In each step, the graph $G_i$ is obtained […]

  • Fluctuation scaling or Taylor’s law of heavy-tailed data, illustrated by U.S. COVID-19 cases and deaths

    Speaker: Joel E. Cohen (Rockefeller University and Columbia University) Title: Fluctuation scaling or Taylor’s law of heavy-tailed data, illustrated by U.S. COVID-19 cases and deaths Abstract: Over the last century, ecologists, statisticians, physicists, financial quants, and other scientists discovered that, in many examples, the sample variance approximates a power of the sample mean of each of a set […]

  • CMSA-QMMP-03.23.2022-1583x2048

    Non-zero momentum requires long-range entanglement

    Youtube Video   Abstract: I will show that a quantum state in a lattice spin (boson) system must be long-range entangled if it has non-zero lattice momentum, i.e. if it is an eigenstate of the translation symmetry with eigenvalue not equal to 1. Equivalently, any state that can be connected with a non-zero momentum state through […]

  • CMSA-NTM-Seminar-03.23.2022-1553x2048-1

    Formal Mathematics Statement Curriculum Learning

    https://youtu.be/4zINaGrPc9M Speaker: Stanislas Polu, OpenAI Title: Formal Mathematics Statement Curriculum Learning Abstract: We explore the use of expert iteration in the context of language modeling applied to formal mathematics. We show that at same compute budget, expert iteration, by which we mean proof search interleaved with learning, dramatically outperforms proof search only.  We also observe that […]

  • CMSA-GR-Seminar-03.24.22

    Rough solutions of the $3$-D compressible Euler equations

    Abstract: I will talk about my work on the compressible Euler equations. We prove the local-in-time existence the solution of the compressible Euler equations in $3$-D, for the Cauchy data of the velocity, density and vorticity $(v,\varrho, \omega) \in H^s\times H^s\times H^{s’}$, $2<s'<s$.  The result extends the sharp result of Smith-Tataru and Wang, established in the irrotational […]

  • CMSA-QMMP-03.24.2022-1583x2048

    Edge physics at the deconfined transition between a quantum spin Hall insulator and a superconductor

    Youtube Video   Abstract: I will talk about the edge physics of the deconfined quantum phase transition (DQCP) between a spontaneous quantum spin Hall (QSH) insulator and a spin-singlet superconductor (SC). Although the bulk of this transition is in the same universality class as the paradigmatic deconfined Neel to valence-bond-solid transition, the boundary physics has a […]

  • CMSA-Active-Matter-Seminar-03.24.22

    Topological defects drive layer formation in gliding bacteria colonies

    Virtual

    Abstract: The developmental cycle of Myxococcus xanthus involves the coordination of many hundreds of thousands of cells aggregating to form mounds known as fruiting bodies. This aggregation process begins with the sequential formation of more and more cell layers. Using three-dimensional confocal imaging we study this layer formation process by observing the formation of holes […]

  • CMSA-Interdisciplinary-Science-Seminar-03.24.2022-1583x2048 (1)

    An operadic structure on supermoduli spaces

    Abstract: The operadic structure on the moduli spaces of algebraic curves  encodes in a combinatorial way how nodal curves in the boundary can be obtained by glueing smooth curves along marked points. In this talk, I will present a generalization of the operadic structure to moduli spaces of SUSY curves (or super Riemann surfaces). This requires […]

  • Periods for singular CY families and Riemann–Hilbert correspondence

    Member Seminar Speaker: Tsung-Ju Lee Title: Periods for singular CY families and Riemann–Hilbert correspondence Abstract: A GKZ system, introduced by Gelfand, Kapranov, and Zelevinsky, is a system of partial differential equations generalizing the hypergeometric structure studied by Euler and Gauss. The solutions to GKZ systems have been found applications in various branches of mathematics including number theory, algebraic geometry and […]

  • Black Hole Spectroscopy

    Abstract: According to general relativity, the remnant of a binary black hole merger should be a perturbed Kerr black hole. Perturbed Kerr black holes emit “ringdown” radiation which is well described by a superposition of quasinormal modes, with frequencies and damping times that depend only on the mass and spin of the remnant. Therefore the observation […]